# Summer Math Research Program

This is the website for the Northeastern Summer Math Research Program (NSMRP), a paid summer program funded by the math department's Research Training Grant.

Other undergraduate math research opportunities at Northeastern.

## Research Experience for Undergraduates

## REU 2024

This program is only for Northeastern students

## Calendar

Mon May 6, 11:30 AM: Kick Off Luncheon

Thurs May 16, 2-3PM: Colloquium (Gabor Lippner)

Fri May 31, 10AM: Preliminary Presentations (20 min/group)

Thurs June 13, 2-3PM: Colloquium (Hunter Dinkins)

Tue June 18, 3-4:30PM: Career/Grad school panel

Fri June 21, 8AM: Final Presentations (45 min/group)

Wed July 3: Final Paper Due

Final Paper: The jointly written paper should be at least 10 pages. Should include an introduction with motivation and guiding questions, definitions, examples, a main result and proof. No maximum page limit, but writing should be clear and concise.

Final Presentation: (45 min for each group) Should introduce audience to area of research, convince them it is interesting through examples, definitions and results. Time is too short to include everything so choose carefully what to present highlighting what you worked hardest on. Narrative and slides and/or boardwork should be clear.

## Research projects and mentors

Participants: Ang Barrett, Daniel Kiem, and Mitchell Wadas

Faculty mentor: Harm Derksen

Graduate student mentor: Shengnan Huang

Participants: Zachary Greenfield, Jonah Marcus, and Jordan Martino

Graduate student mentors: Sean Carroll and Vitor Gulisz

Participants: Aden Lu and Roland Waterson

Graduate student mentor: Yujia Shi

Participants: Aidan Tillman and Yuzhi Liu

Faculty mentor: Stuart Brorson

Graduate student mentor: Zhaoming Li

Participants: Jacob Ginesin and Daniel Yu

Faculty mentor: David Rosen

Graduate student mentors: Forrest Miller

Participants: Walla Rahama and Ishan Thakur

Faculty mentor: Milen Yakimov

Graduate student mentor: Yunmeng Wu

Participants: Devin Brown, Emily Fink, and Naiwen Wang

Faculty Mentor: Vance Blankers

Graduate student mentor: Rahul Hirwani

Participants: Abby Jiang and Nicholas Sokolovic

Graduate student mentor: Arturo Ortiz San Miguel

Post-doc coordinators: Hunter Dinkins and Josh Wen

Faculty organizers: Harm Derksen, Iva Halacheva, Valerio Toledano Laredo, and Xuwen Zhu

## REU 2023

Additional funding for the Summer 2023 program was provided by the College of Science and Department of Mathematics.

## Research projects and mentors

Participants: Tao (Luisa) Li, Aaron Soice, and Ryan Zhu

Mentor: Olakunle Abawonse

Paper: Group equivariant neural networks

Participants: Evelyn Brylow, Timothy Demling, Walla Rahama, and Nicholas Sokolovic

Mentors: Sean Carroll and Hunter Dinkins

Paper: P-adic numbers

Chemical reaction networks and monotone dynamical systems

Participants: Edward Berman and Anna XiaMentor: Alon DuvallAffiliated faculty: Eduardo D. Sontag and M. Ali Al-RadhawiPaper: Sufficient conditions for monotonicity in stochastic chemical reaction networksParticipants: Devin Brown, Daniel Kiem, and Jordan Martino

Mentor: Shengnan Huang

Affiliated faculty: Milen Yakimov

Paper: Combinatorial construction of nilpotent Lie algebras

Participants: Zachary Greenfield and Zoey Yelsky

Mentor: M. Anadil Saeed Rao

Paper: Representations of the Virasoro algebra

Participants: Jonah Marcus and Molly Sager

Mentor: Ahmad Reza Haj Saeedi Sadegh

Post-doc coordinator: Josh Wen

Faculty organizers: Iva Halacheva, Valerio Toledano Laredo, and Xuwen Zhu

## REU 2022

In light of the COVID-19 pandemic, this program was held remotely.

## Research projects and mentors

### Equivalent matroids arising from graphs

Participants: Jiaqi Lu and Brandon Onyejekwe Mentor: K. Finn PrideauxPaper: Equivalent matroids arising from graphsFinal presentation slides### Morita theorems

Participants: Nicholas Bidorini and Zach Greenfield

Mentor: Vitor Emanuel Gulisz

Paper: The Morita theorems

### Regularization and renormalization in quantum field theory

Participants: Daniel Abadjiev, Anthony Melo, and Zhengxun Liu

Mentor: M. Anadil Saeed Rao

Paper: Renormalization and regularization of φ^4 and φ^3 scalar quantum field theories

### Graph bootstrap percolation

Participants: Andy Babb, Stephanie Martinez, and Timothy Wang

Mentor: Connor Anderson

Paper: Approximation of spread minimization in bootstrap percolation

### Knot polynomials and Khovanov homology

Participants: Jordan Martino and Francisco Turdera

Mentor: Ryan Kannanaikal

Post-doc coordinators: Iva Halacheva, Matej Penciak, Josh Wen

Faculty organizer: Valerio Toledano Laredo

## REU 2021

In light of the COVID-19 shutdown, this program was held entirely remotely.

Additional funding for the Summer 2021 program was provided by the College of Science and Department of Mathematics.

## Calendar

Mon May 10, 9 AM: Kick Off Meeting

Thu May 20, 10-11 AM: Colloquium

Thu June 3, 10 AM: Preliminary Presentation (20 min/group)

Thu June 17, 10 AM: Colloquium

Tue Jun 29, 8 AM: Final Presentations (45 min/group)

Tues July 6: Final Paper Due

Final Paper: The jointly written paper should be at least 10 pages. Should include an introduction with motivation and guiding questions, definitions, examples, a main result and proof. No maximum page limit, but writing should be clear and concise.

Final Presentation: (45 for each group) Should introduce audience to area of research, convince them it is interesting through examples, definitions and results. Time is too short to include everything so choose carefully what to present highlighting what you worked hardest on. Narrative and slides and/or boardwork should be clear.

## Groups

### Configuration spaces of points and lines

Participants: Luke Boyer, Shane Calle, Nick Payne. Mentor: Ian Dumais

Paper: Configurations of Lines and Spaces

### Probabilistic simulations of IOTA cryptocurrency

Participants: Maria Candello, Grant Chau, Jiachen Xu. Mentor: Anupam Kumar

Paper: Probabilistic Simulations of IOTA Cryptocurrency

### Modeling of random geometric graphs

Participants: Maitreyee Joshi, Nicholas Thevenin, Bryan Vogt. Mentor: Hiu Ying Man

Paper: Extending Bottleneck Matching and Monotone Property Threshold Width to the Torus

### Chromatic numbers of fractional power graphs

Participants: Luke Drennen, Noah Lichtblau. Mentor: Finn Prideaux

Paper: Chromatic Numbers and K-Connectivity of Graph Fractional Powers

Post-doc coordinators: Vance Blankers, Matej Penciak

Faculty organizer: Valerio Toledano Laredo

## REU 2020

In light of the COVID-19 shutdown, this program was held entirely remotely.

## Calendar

Mon May 4, 9AM: Kick Off Meeting

Mon May 18, 2PM: Preliminary Presentation (20 min/group)

Wed May 27, 2-3PM: Colloquium

Wed June 17, 2-3PM: Colloquium

Thr Jun 25, 2PM: Final Presentations (45 min/group)

Fri July 3: Final Paper Due

Final Paper: The jointly written paper should be at least 10 pages. Should include an introduction with motivation and guiding questions, definitions, examples, a main result and proof. No maximum page limit, but writing should be clear and concise.

Final Presentation: (45 for each group). Should introduce audience to area of research, convince them it is interesting through examples, definitions and results. Time is too short to include everything so choose carefully what to present highlighting what you worked hardest on. Narrative and slides and/or boardwork should be clear.

## Groups

### Evolutionary Dynamics.

Participants: Jack Steilberg, Lauren Neudorf. Mentor: Jonier Antunes.

Paper: Infinite Random Graphs and Evolutionary Dynamics

### Spectral Graph Theory.

Participants: Ryan Keleti, Noble Mushtak. Mentor: Whitney Drazen.

Paper: Fractional Revival and Fractional Cospectrality

### Elliptic Curves.

Participants: Zoe Daunt, Xiaoying He, Xuyang Li. Mentor: Lei Yang.

Paper: Elliptic Curves and Probability of $\ell$-torsion

Post-doc coordinators: Rob Silversmith, Robin Walters

Faculty organizer: Valerio Toledano Laredo

## REU 2019

## Calendar

May 6: First Official REU Meeting (Summer I)

May 13: Proposal Draft

May 28: REU Tea & Colloquium 3-4 PM, Lake 509

June 4: REU Tea & Group Presentations 3-4 PM, Nightingale 544

June 11: REU Tea & Colloquium 3-4 PM, Lake 509

June 21: Final Presentations, Lunch 12-1, Talks 1-4, Lake 509 (Summer I)

June 28: Final Paper Due (Summer I)

August 14: Final Presentations (Summer II)

Final Paper: At least 5 pages. If two students, then paper is written together is at least 10 pages. Should include an introduction with motivation and guiding questions, definitions, examples, a main result and proof. No maximum page limit, but writing should be clear and concise.

Final Presentation: 30 minutes (40 if group of 2). Should introduce audience to area of research, convince them it is interesting through examples, definitions and results. Time is too short to include everything so choose carefully what to present highlighting what you worked hardest on. Narrative and slides and/or boardwork should be clear.

## Groups

### Evolutionary Dynamics.

Participants: Hoyin Chu. Mentor: Jonier Antunes. Summer I.

Paper: Introduction to Evolutionary Dynamics and Stochastic Calculus.

### Knot Theory.

Participants: Noah Fleischmann, Kally Lyonnais. Mentor: Dmytro Matvieievsky. Summer I.

Paper: Knots, Colors, and Polynomials.

### Graph Theory/Chip Firing:

Participants: Kristin Timothy, Michael Wang. Mentor: Ian Dumais. Summer I.

Paper: Sandpiles and Chip Firing.

### Homotopical Algebra:

Participants: Karthik Boyareddygari Mentor: Oleksiy Sorokin. Summer I.

Paper: Homotopical Approach to Tensor Products.

### Algebraic Geometry:

Participants: Walker Miller-Breetz. Mentor: Anupam Kumar. Summer II.

Paper: Cone Points on Algebraic Curves.

Post-doc coordinators: Emily Barnard, Rob Silversmith, Robin Walters

Faculty organizer: Valerio Toledano Laredo

## REU 2018

The inaugural year of the Northeastern REU had 9 undergraduate participants working in several different areas. The postdoc coordinator was Ivan Martino.

Student: Alon Duvall

Mentor: Brian Hepler

Title: Abstract Regular Polytope

Abstract: Introduction to Abstract Regular Polytopes through a combinatorial geometry approach. C-Groups, Coxeter Groups and 2^k-constructions are also studied.

Student: Kevin Su

Mentor: Jonier Antunes

Title: Graph Limits and Extremal Combinatorics

Abstract: "One of the problems in extremal combinatorics is asking how many edges a graph on n nodes may have while avoiding some speciﬁc subgraphs. For example, Mantel’s theorem says that the most edges a graph on n nodes can have while avoiding K_3 is n^2/4. These statements can also be represented in terms of inequalities of numbers of homomorphisms or in terms of homomorphism densities. Many of these inequalities may be proved using Cauchy-Schwarz (as an inequality on sums of squares) or pictorially due to a gluing algebra on the space of graphs. We summarize some of the graph algebra background involved here and look at how graph limit theory gives a way of proving results in extremal combinatorics."

Student: Timothy Jackman

Mentor: Whitney Drazen

Title: Graph Theory

Abstract: This is an introduction to spectral graph theory until the concepts of (quantum) state transfer.

Student: Felipe Castellano-Macias

Mentor: Alex Sorokin

Title: Leavitt Path Algebras

Abstract. We describe diﬀerent properties of Leavitt path algebras of a graph over a ﬁeld, providing the appropriate background. In addition, we investigate similar results about Leavitt path algebras of a graph over a commutative unital ring. We will mainly explore the connection between the diagonalizability of matrices over a given Leavitt path algebra and the structure of its underlying graph, as well as the classiﬁcation of such algebras up to isomorphism.

Name: Benjamin Bonenfant

Mentor: Reuven Hodges

Student: Walker Miller-Breetz

Mentor: Rahul Singh

Title: Young Tableaux

Abstract: After a short introduction on group theory and group actions, the work focuses on the symmetric group and its action on flagged spaces.

Student: Christina Nguyen

Mentor: Whitney Drazen

Title: Non-backtracking Walks on Graphs

Abstract: The main goal of the REU was to obtain a new proof of the non-backtracking version of Ploya’s Theorem for random walks. We began with a discussion of spectral graph theory before studying the backtracking version of Ploya’s Theorem.

Student: Noah Lichtblau

Mentor: Mikhail Mironov

Title: On the Morphism of Schemes

Student: Zheying Yu

Mentor: Celine Bonandrini

Title: Topology

Faculty Organizer: Emanuele Macri

## Calendar

Mon May 9, 9:30 AM: Kick Off Meeting

Wed May 18, 3-4 PM: Colloquium

Wed May 25, 3-4 PM: Colloquium

Fri June 3, 10 AM: Preliminary Presentations (20 min/group)

Wed June 8, 3-4 PM: Colloquium

Wed June 15, 3-4 PM: Colloquium

Fri Jun 24, 9 AM: Final Presentations (45 min/group)

Wed July 6: Final Paper Due

Final Presentation: (45 min for each group) Should introduce audience to area of research, convince them it is interesting through examples, definitions and results. Time is too short to include everything so choose carefully what to present highlighting what you worked hardest on. Narrative and slides and/or boardwork should be clear.